When we use range finders to observe the shape of an object, many occluded areas may occur. Thesebecome holes and gaps in the model and make it undesirable for various applications. We propose a novelmethod to fill holes and gaps to complete this incomplete model. As an intermediate representation, weuse a Signed Distance Field (SDF), which stores Euclidean signed distances from a voxel to the nearestpoint of the mesh model. By using an SDF, we can obtain interpolating surfaces for holes and gaps. Theproposed method generates an interpolating surface that becomes smoothly continuous with real surfacesby minimizing the area of the interpolating surface. Since the isosurface of an SDF can be identified asbeing a real or interpolating surface from the magnitude of signed distances, our method computes thearea of an interpolating surface in the neighborhood of a voxel both before and after flipping the sign ofthe signed distance of the voxel. If the area is reduced by flipping the sign, our method changes the signfor the voxel. Therefore, we minimize the area of the interpolating surface by iterating this computationuntil convergence. Unlike methods based on Partial Differential Equations (PDE), our method does notrequire any boundary condition, and the initial state that we use is automatically obtained by computingthe distance to the closest point of the real surface. Moreover, because our method can be applied to anSDF of adaptive resolution, our method efficiently interpolates large holes and gaps of high curvature.We tested the proposed method with both synthesized and real objects and evaluated the interpolatingsurfaces.

INDEX TERMS

3D modeling, interpolation of a mesh model, adaptive signed distance field